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1 Unitat Biofísica i Bioenginyeria, Facultat Medicina, Universitat Barcelona-IDIBAPS and 2 Hospital Clínic, 08036 Barcelona, Spain; 3 School of Biomedical Engineering, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5; and 4 Harvard School of Public Health, Boston, Massachusetts 02115
Magnetic twisting
cytometry (MTC) (Wang N, Butler JP, and Ingber DE, Science
260: 1124-1127, 1993) is a useful technique for probing cell
micromechanics. The technique is based on twisting ligand-coated
magnetic microbeads bound to membrane receptors and measuring the
resulting bead rotation with a magnetometer. Owing to the low
signal-to-noise ratio, however, the magnetic signal must be modulated,
which is accomplished by spinning the sample at ~10 Hz. Present
demodulation approaches limit the MTC range to frequencies <0.5 Hz. We
propose a novel demodulation algorithm to expand the frequency range of
MTC measurements to higher frequencies. The algorithm is based on
coherent demodulation in the frequency domain, and its frequency range
is limited only by the dynamic response of the magnetometer. Using
the new algorithm, we measured the complex modulus of elasticity
(G*) of cultured human bronchial epithelial cells (BEAS-2B) from 0.03 to 16 Hz. Cells were cultured in supplemented RPMI medium, and
ferromagnetic beads (~5 µm) coated with an RGD peptide were bound
to the cell membrane. Both the storage (G', real part of G*) and loss
(G", imaginary part of G*) moduli increased with frequency as
(2
× frequency) with 
1/4. The ratio G"/G' was ~0.5 and varied little with
frequency. Thus the cells exhibited a predominantly elastic behavior
with a weak power law of frequency and a nearly constant proportion of
elastic vs. frictional stresses, implying that the mechanical behavior
conformed to the so-called structural damping (or constant-phase) law
(Maksym GN, Fabry B, Butler JP, Navajas D, Tschumperlin DJ, LaPorte JD,
and Fredberg JJ, J Appl Physiol 89: 1619-1632,
2000). We conclude that frequency domain demodulation dramatically
increases the frequency range that can be probed with MTC and reveals
that the mechanics of these cells conforms to constant-phase behavior
over a range of frequencies approaching three decades.
cell mechanics; cell viscoelasticity; complex elastic modulus; power law rheology; structural damping; magnetic tweezers
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